Ramsey theory of trees
Speaker:
Spencer Unger, University of Toronto
Date and Time:
Friday, December 9, 2022 - 1:30pm to 3:00pm
Location:
Fields Institute, Room 210 or online at https://zoom.us/j/92415047239
Abstract:
We make several observations about the infinite dimensional Ramsey theory of trees. To start we define a weakening of a Ramsey space and give a natural class of examples these spaces which do not satisfy Todorcevic's axioms (in particular the amalgamation axiom fails). Motivated by these examples, we give a classical proof of a version of the Halpern-Lauchli theorem which allows us to analyze spaces of copies of the rationals and more generally SDAP classes of Coulson-Dobrinen-Patel. This is joint work with Stevo Todorcevic.